Both clubs have been linked with moves for the Dundee forward, who's turned down the offer of a new contract at Dens Park.
Having entered the final year of his existing deal, it seems increasingly unlikely that Stewart will still be a Dundee player in 12 months' time.
The Dark Blues are said to value the 26-year-old, who scored 11 goals last season in all competitions, at £1.5 million.
However, he would be eligible to sign a pre-contract agreement with other clubs from January, should any interested parties fail to match Dundee's demands.
And Stewart's comments suggest he would welcome a change of scenery.
"Sometimes I think 'wow' - three years ago I was working at Grangemouth (oil refinery) and now top teams like Leeds United and Rangers are interested in me," he told the Dundee Evening Telegraph.
"Put it this way, I don’t want to go back to the oil refinery any time soon. I have to pinch myself sometimes when I think about it.
"I want to be somewhere I can play my best football. Whether it is at Dundee we will just have to wait and see.
"I have ambitions, just like most people. I want to play at the highest level I possibly can."
The Daily Record reports that Rangers boss Mark Warburton hopes to add a new striker to his ranks this week, though whether or not Stewart would fit the bill remains to be seen, having spent much of last season as a left-side forward.
Leeds, meanwhile, have captured two attackers in the space of a week, with winger Hadi Sacko following Swedish striker Marcus Antonsson to Elland Road.
Hadi Sacko (right)